2 November 2015
Does the proportion of human cases attributed to each source change seasonally?
Did the intervention in the poultry industry work?
Is attribution related to rurality?
Do some genotypes cause human disease more than others?
Work with Poppy Miller and Chris Jewell, generalising the modified Hald model of Müllner et. al. 2009.
Model human cases \(Y_{itl}\) of genotype \(i\) at time \(t\) in location \(l\) by \[ Y_{itl} \sim \mathsf{Poisson}(q_i \sum_j a_{jtl} p_{ijt}) \]
\[ P(\mathsf{st}) = \sum_j P(\mathsf{st} \mid \mathsf{source}_j) P(\mathsf{source}_j) \]
\[ P(\mathsf{st}) = \sum_j \underbrace{P(\mathsf{st} \mid \mathsf{source}_j)}_\text{genomic model} P(\mathsf{source}_j) \]
\[ P(\mathsf{st}) = \sum_j \underbrace{P(\mathsf{st} \mid \mathsf{source}_j)}_\text{genomic model} \underbrace{P(\mathsf{source}_j)}_\text{attribution to source} \]
\[ \begin{aligned} &P(\mathsf{st} \mid \underbrace{t, \mathbf{x}}_\text{covariates}) =\\ &\quad \sum_j \underbrace{P(\mathsf{st} \mid \mathsf{source}_j)}_\text{genomic model} \underbrace{P(\mathsf{source}_j \mid t, \mathbf{x})}_\text{attribution with covariates} \end{aligned} \]
Nested within each source \(j\) we have \[ \begin{aligned} \mathsf{logit}\left(P(\mathsf{source}_j \mid t, \mathbf{x})\right) &= \mathsf{Location}_\mathbf{x} \cdot \mathbf{1}\left[t \geq 2008\right] \cdot \mathsf{Month}_t + \epsilon_{\mathbf{x}t}\\ \epsilon_{\mathbf{x}t} &\sim \mathsf{Normal}(\rho \epsilon_{\mathbf{x}(t-1)}, \sigma^2) \end{aligned} \]
Covariates are estimated as a Gibbs step conditional on correlation \(\rho\), variance \(\sigma^2\) and \(P(\mathsf{source}_j \mid t, \mathbf{x})\).
\(\phi\) and \(\sigma^2\) are then updated using Gibbs conditional on the covariates and \(P(\mathsf{source}_j \mid t, \mathbf{x})\).
\(P(\mathsf{source}_j \mid t, \mathbf{x})\) are then updated from the full conditional prior, interleaved with Metropolis Hastings steps.
Urban cases tend to be more associated with poultry, and rural cases with ruminants.
There does seem to be some evidence for seasonality in attribution.
The poultry intervention in 2007 resulted in a marked reduction in poultry related cases in urban areas, less strong in rural areas.
Very few cases associated with water or other sources.
Limitation: Genomic model assumed constant through time.
Two R packages are on the way, sourceR and islandR.
Slides: http://bit.ly/1MnICKi
Twitter: @jmarshallnz
Github: jmarshallnz